Morning Mathematical Monsters & Maniacs!
(Today’s post is sponsored by the letter “M”)
Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.
And what better way to start your week, then by discussing math Monday morning?
While celebrating Pi day a couple weeks ago, we discussed how it is an irrational number that cannot be expressed as a fraction. This week we look at fractions.
A fraction represents a part of a whole. It comes from the latin word fractus, meaning broken. Fractions are commonly expressed in the form a/b, where b is not equal to 0. In the form a/b, a is known as the numerator and b as the denominator.
As far back as 4,000 years ago, the Egyptians used what is now known as Egyptian fractions. Egyptian fractions are reciprocals of integers. Egyptian fractions were 1/2, 1/3, 1/4, 1/5, … However, they did not use the modern day a/b notation that is now used.
The a/b notation with a horizontal bar separating the numerator and denominator dates back to the 12th century when Muslim mathematician Abu Bakr Muhammad ibn Abdallah ibn Ayyash al-Hassar (better known as just Al-Hassar) first used the notation in Moracco. His notation quickly became popular and was widely used in the following century, most notably thanks to Italian mathematician Leonardo Fibonacci (pictured below). Fibonacci popularized the Hindu–Arabic numeral system in the Western World primarily through his 1202 publication of Liber Abaci, meaning Book of Calculation.
In Postcards From the Wedge (Season 21, Episode 14), Bart tells us how much he detest fractions:
Bart: “I would end all life on this planet just to get out of doing fractions.”
Lisa: “Fractions aren’t that hard. You just have to have a common denominator. For example, one-half plus one-third equals three-…”
Bart: “End. all. life. on. this. planet!” [makes explosion sound]
Lisa: “You’ll need to know fractions to make that explosion!”
But only three seasons later, in Adventure’s in Baby-Getting (Season 24, Episode 03), after Homer fails to fix a leak in the hose faucet, the ground under Springfield collapses from the mass of the pooling water and causes a sinkhole in the middle of the city. Marge, Lisa, and Bart are driving to school when Marge’s car falls through the sinkhole as the ground collapses and ruins her car. But just before the car falls through, we get a glimpse at Bart’s math homework.
Like Lisa said, fractions aren’t hard, you just need to find a common denominator (for addition and subtraction). Fortunately for us, every question has a common denominator. Lets go ahead and work through Bart’s homework.
When adding fractions with common denominators, you simply have to add the numerators to obtain the new numerator, while the denominator remains the same. Questions 1 and 4 feature addition:
5/8 + 1/8 = 6/8 (6/8 can be reduced by dividing both numerator and denominator by 2 to get 3/4)
4/12 + 7/12 = 11/12
Subtracting fractions is essentially the same as adding. When subtracting fractions with common denominators, you simply have to subtract the numerators to obtain the new numerator. Question 2 features subtraction:
3/7 – 2-7 = 1/7
Multiplying fractions does not require common denominators. You simply multiply the numerators to obtain the new numerator and multiply the denominators to obtain the new denominator. Question 5 features multiplication:
3/6 x 7/6 = 21/36 (21/36 can be reduced by dividing both numerator and denominator by 3 to get 7/12)
Dividing fractions, like multiplying fractions, does not require common denominators. You simply multiply the first fraction by the reciprocal of the second fraction. Question 3 features division:
5/4 ÷ 3/4 = 5/4 x 4/3 = 20/12 (20/12 can be reduced by dividing both numerator and denominator by 4 to get 5/3)
Now that we’ve got a better understanding of fractions and looked at Bart’s homework, are you reminded of your days in math class? Did you remember this episode? Were you able to solve the problems on your own? Do you enjoy calculating with fractions? Sound off in the comments below. You know we love hearing from you.